Treeness

A tree may, for the imagination, present forcibly one of its qualities at a time; it may be a green dome of shade on a hot day, a ladder of retreat for a man from the attentions of a mad bull, a peg on which an apple hangs, a screen for an assassin, a choir for birds; and its own business of spreading out its million pores to the air and propagating its kind, which comes nearest to being its “treeness,” may be what occupies the artist least and bores him most.

A word represents the entity but not THE entity itself. "tree" is not a tree, you can call it "ca^y" or whatever but the conceptual meaning of treeness stays the same.

Let us say that the pigeons learned to recognize treeness, in the sense that they quickly enough learned to differentiate whatever exemplified treeness from whatever did not.

If factors that contribute to a tree-like pattern of the variance–covariance matrix dominate the evolutionary picture over those that tend to destroy it, one can expect treeness to be reasonably high. Only if this is true, reconstruction of the evolutionary process by tree analysis and a tree representation for descriptive purposes can be useful.

The computer programs used to generate “trees” from genetic distance data will do so regardless of what evolutionary factors generated the distances. It is therefore the obligation of the users of such programs to ensure that the genetic distance data have the properties of treeness before representing their data as a tree.

Failing to statistically test for treeness, they reify the evolutionary trajectories assumed at the outset.

…such a tree can be built up incrementally by adding the shortest edge not yet explored, which also maintains treeness (acyclicity).

…every link that gives rise to a cycle into the graph (viz., that destroys the graph’s “treeness”) is eliminated….